The Canadiens still lead the conference with a 14-5-4 mark. They next play at Carolina on Thursday before heading to play at Tampa Bay and Florida over the weekend.
Martin scored at 12:10 of the second, knocking in a pass from Brad Boyes for his second of the season with Montreal's Lars Eller serving a tripping penalty. Grabner added his ninth of the season at 12:58 after a shot by defenseman Thomas Hickey deflected to him in front of Price.
Montreal's Tomas Plekanec opened the scoring at 5:21 of the first with his 10th of the season. Plekanec took a pass from Alex Galchenyuk in the left corner after Michael Ryder outmuscled Martinek in the right corner.
Matt Moulson tied it at 1:23 of the second off a pass from defenseman Mark Streit for his 11th of the season.
The Islanders have won three straight and six of their last eight games against Montreal, including 4-3 in overtime at Montreal on Feb. 21. The teams meet once more this season at Nassau Coliseum on March 21.
It was the fifth contest of a seven-game homestand for the Islanders, who host the Rangers on Thursday before completing the homestand Saturday against Washington.
"Having the Rangers here will be intense," Martinek said. "All we can do is continue playing the way we have these past two here at home. It's really a simple game. You have to play hard every night."
NOTES: The Islanders played without D Lubomir Visnovsky, who had to attend to a family matter . LW Moulson's games-played streak stands at 269 games. He has yet to miss a game in his Islanders career . Mike Cammalleri scored the 20,000th goal in Canadiens history on Dec. 28, 2009. The franchise also played eight seasons starting in 1909-10 in the NHL's predecessor, the National Hockey Association.